5168
J. Phys. Chem. A 1997, 101, 5168-5173
Classical Trajectory Study of Mode Specificity and Rotational Effects in Unimolecular
Dissociation of HO2
J. M. C. Marques and A. J. C. Varandas*
Departamento de Quı́mica, UniVersidade de Coimbra, P-3049 Coimbra Codex, Portugal
ReceiVed: March 17, 1997; In Final Form: May 7, 1997X
Trajectory calculations are presented for the unimolecular dissociation of HO2. The study covers internal
energies in the range 58.311 e Etot/kcal mol-1 e 59.432, just above the H + O2 threshold, and Etot ) 76.412
kcal mol-1 for which the O + OH channel is also open. The HO2 single-valued double many-body expansion
potential energy surface has been employed in all calculations. Due to strong coupling among the vibrational
degrees of freedom, mode specificity is shown to play a minor role in the formation of H + O2. Conversely,
the increase of initial rotational energy clearly influences the dynamics of the unimolecular dissociation. In
particular, energy placed in a specific rotational degree of freedom can dramatically modify the yield of O2
or OH products and corresponding decay rates. The results show the importance of rotational effects in
order to correctly describe the unimolecular dissociation of HO2.
1. Introduction
the past few years on the dissociation reaction
Unimolecular systems are usually employed in the study of
energy transfer phenomena among internal degrees of freedom.
In this context, most published theoretical work has focused
on topics such as intramolecular vibrational energy redistribution, isomerization between two minima of the potential surface,
nonlinear processes and chaos, and unimolecular dissociation.
Since the number of degrees of freedom increases with the
number of atoms in the molecule, tetratomic and larger
molecules are usually employed in such studies. However,
having only three (four) vibrational modes, nonlinear (linear)
triatomic molecules can provide a more clear understanding of
unimolecular processes (e.g., refs 1 and 2 and references
therein).
The Rampsberger-Rice-Kassel-Marcus (RRKM) theory3,4
has been successfully applied in the study of a wide variety of
unimolecular reactions. This statistical theory is based on the
assumption that intramolecular energy redistribution is rapid in
comparison with the reaction time. Thus, non-RRKM behavior
is associated with the fact that modes relax at different rates,
and coupling between different degrees of freedom depends both
on its nature and level of excitation, which may originate
nonlinear resonances. In other words, intramolecular energy
transfer occurs via specific pathways. A well-studied situation
favoring rate enhancement by specific mode excitation is the
reaction over a low potential barrier, which has been explored
by Thompson and co-workers5,6 in their studies of HONO cistrans isomerization. The HONO molecule has also been used
to investigate the influence of rotation and angular momentum
orientation in the rate of dissociation.7 More recently, Marks8
has searched for mode-specific effects in the isomerization of
CD2HNC and found that rotational excitation about the molecular axis enhances the corresponding rates.
Rotational effects on the unimolecular dissociation of the HO2
system have been previously reported by Miller and Brown9
using the Melius-Blint10 potential energy surface, which shows
an unphysical barrier for dissociation into H + O2. However,
it has been the emergence of a realistic single-valued double
many-body expansion11 potential surface for HO2 (known as
DMBE IV) that induced considerable theoretical interest during
X
Abstract published in AdVance ACS Abstracts, June 15, 1997.
S1089-5639(97)00960-2 CCC: $14.00
HO*
2 f O2 + H
(1)
The star in HO*2 implies an energized species. Recently,
Mandelshtam et al.12 have reported a detailed investigation of
bound states and resonances for the nonrotating (J ) 0)
hydroperoxyl radical up to an energy just above the H + O2
dissociation threshold and concluded that the HO2 system is
dominantly irregular, especially at high energies close to the
dissociation threshold. Motivated by this work, Mahapatra13
has shown that the time domain behavior of the bound states
and resonances of the HO2 radical is extremely chaotic, which
is in excellent agreement with the corresponding Wigner nearestneighbor spacing distributions reported by Mandelshtam et al.12
and by Dobbyn et al.14 Moreover, these authors15 have
concluded that the HO2 system is classically chaotic (at energies
near the H + O2 threshold), presenting strong fluctuations on
the resonance widths and random lifetime distributions of the
classical trajectories. However, Dobbyn et al.14 have also found
that, although the wave functions are mostly irregular around
the H + O2 dissociation threshold, there are some regular states
that are associated with extensive excitation in the OO stretching
mode. Indeed, using quantum and semiclassical variational
transition state models, Song et al.16 have calculated microcanonical rate constants for reaction 1, and concluded from a
comparison of the different results that there is weak coupling
between the OO stretching and OOH bending modes along the
reaction path. Moreover, we have recently found17 that dissociation of energized HO*
2 complexes arising from H + ArO2
collisions follows essentially a non-RRKM behavior, which
could apparently be due to vibrational mode specificity.
In this work, we report a classical dynamics study of the
unimolecular dissociation for internal energies in which reaction
1 is the only open channel and also for formation of both H +
O2 and O + OH products. Our main goals are to study the
effect of rotation in HO*
2 unimolecular dissociation and search
for vibrational mode specificity in this reactive process. Thus,
after a brief presentation of the methodology in section 2, the
results are reported and discussed in section 3. Section 4
summarizes the conclusions.
© 1997 American Chemical Society
Unimolecular Dissociation of HO2
J. Phys. Chem. A, Vol. 101, No. 28, 1997 5169
a
TABLE 1: Results of the Trajectory Calculations for the Nonrotating HO*
2 Molecule
H + O2 products
Etot/kcal mol
59.432
59.432
58.857
58.780
58.311
c
-1
(ν1, ν2, ν3)
c
(3,3,3)
(16,0,0)
(0,13,0)
(0,0,5)
b
Nisom
f〈E′v〉
f〈E′r〉
f〈E′tr〉
kb/ps-1
1985(3)
1970(3)
2400(4)
2744(5)
2353(4)
0.37
0.39
0.36
0.37
0.38
0.04
0.04
0.04
0.04
0.04
0.59
0.57
0.60
0.59
0.58
0.91
0.92
0.68
0.68
0.69
a All energies are above H + O and below O + OH dissociation thresholds. b Total number of isomerizations for trajectories forming H + O .
2
2
Initial conditions chosen using a microcanonical sampling procedure.
2. Method
All calculations reported in the present work have employed
the DMBE IV11 potential energy surface for the electronic
ground state of the HO2 radical. For the purpose of the present
calculations, its most relevant features are the two deep
equivalent wells associated with the corresponding HO2 isomers,
which are separated by a saddle point structure. Since the
DMBE IV potential energy surface has been extensively used
for dynamics studies11,17-26 involving the HO2 radical, we omit
here any further details.
The classical trajectory method has been employed to
calculate the unimolecular decay rates for reaction 1. All
calculations have been done using an adapted version of the
MERCURY27 computer code to run batches of typically 500
trajectories for various selected initial vibrational and rotational
energies. After proper optimization the integration step has been
fixed at 3.0 × 10-17 s. Trajectories are considered to be reactive
whenever the forming products are separated by more than 5
Å. Nondissociative trajectories are allowed to last up to 60 ps.
To define the initial conditions, we have assigned vibrational
quanta (ν1, ν2, ν3) to each normal mode with random vibrational
phases28,29 or, alternatively, used a microcanonical sampling
method to distribute the vibrational energy among the three
modes. Thus, the vibrational energy is given by the sum of
the three normal mode energies
Ev ) EOO + EOOH + EOH
(2)
being the fundamental frequencies 1101, 1353, and 3485 cm-1
for OO stretching, OOH bending, and OH stretching, respectively. Once the normal mode energies have been assigned,
the nonseparable Hamiltonian of the system is calculated and
the Cartesian coordinates and momenta are scaled to give the
required vibrational energy30 within a tolerence of ∼10-3 kcal
mol-1 or so. During the scaling procedure, spurious linear and
angular momenta created in the molecule by the vibrational
excitation are removed.
The rotational energy assignment has been done by calculating the magnitude of the angular momentum vector corresponding to the specified rotational energy, Er. Since the vibrational
angular momentum has already been removed, one has
1
Er ) LTI-1L
2
(3)
where LT is the transpose of the angular momentum vector and
I-1 is the inverse of the momentum of inertia tensor, which is
calculated for every specific initial geometry of the molecule
after the assignment of the vibrational energy. Note that the
axis of rotation is defined by the orientation of the total angular
momentum, and hence it is established by providing the
corresponding direction cosine vector D. Thus, using eq 3, the
magnitude of the total angular momentum is given by
|L| )
(
2Er
)
1/2
(4)
DTI-1D
where it is implicit that each component of L can be written as
Li ) |L|Di
(5)
Each of the three direction cosine components (Di) may then
be specified as 0 or 1, according to the selected orientation for
the L vector, and multiplied by the appropriate 1/(∑iDi)1/2
normalizing factor. Finally, the angular velocity can be written
in matrix form as
ω ) I-1L
(6)
and the velocity ω × Ri due to rotation added to each atom; Ri
is the position vector of the ith atom.
After the trajectories have been calculated for different sets
of initial conditions, it is possible to characterize the dissociation
behavior of HO*
2 and obtain the corresponding rates. To describe
non-RRKM behavior in the decaying molecules, we have
considered the following two-step mechanism17
ka
kb
A 98 B 98 products
(7)
where A (B) stands for HO*2 molecules not coupled (strongly
coupled) with the reaction path and the rate coefficients follow
the relation ka < kb or ka , kb. Using such a scheme, the
calculated fraction of HO*2 molecules present at each moment
can be fitted to the form17
(
f(t) ) fA + fB ) f 0B -
)
(
kaf 0A
exp(-kbt) +
kb - ka
)
kaf 0A
+ f 0A exp(-kat) (8)
kb - ka
where fA and fB are the fractions of A and B at time t and f 0A
and f 0B are the corresponding values for t ) 0; f 0A, f 0B, ka, and
kb are adjustable parameters. Thus, if the kinetics is essentially
RRKM type, it can be described using
f(t) ) f 0B exp(-kbt)
(9)
where it has been assumed that all HO*
2 molecules are B-type
(i.e., f 0A ) 0); see also ref 17.
3. Results and Discussion
Mode specificity in HO*
2 dissociation has been investigated
for the nonrotating system with internal energies varying from
58.311 to 59.432 kcal mol-1. The results are presented in Table
5170 J. Phys. Chem. A, Vol. 101, No. 28, 1997
Marques and Varandas
Figure 1. Schematic representation of the three normal modes of vibration for HO2 shown in the system of coordinates associated to the principal
axis of inertia: (a) OO stretch, (b) OOH bend, and (c) OH stretch. Note that the x-axis and y-axis are represented by dashed lines, while the z-axis
is perpendicular to the plane of the figure. For clarity, the oxygen atoms are shown by the shadowed circles, and the hydrogen atom is represented
by the open one.
1 and comprise the number of HOaOb f HObOa (a and b label
the O atoms) isomerizations, the average fractions of vibrational,
rotational, and translational energies in the products, and the
values of the dissociation rate coefficients kb. Four different
sets of initial vibrational quantum numbers (ν1, ν2, ν3) have
been investigated, in addition to a microcanonical distribution
of the vibrational energy. Table 1 shows that the total number
of isomerizations (the average number of isomerizations per
trajectory is given in parentheses) increases with excitation of
the bending mode; for a pictorial representation of the normal
mode eigenvectores, see Figure 1. Moreover, we observe a
decrease in the total number of isomerizations when passing
from the (16,0,0) to the (0,0,5) excitation, as might be anticipated
from the inspection of the corresponding eigenvectors for the
OO (Figure 1a) and OH (Figure 1c) stretching modes. In
addition, there is a decrease in the number of isomerizations
(the average value per trajectory is now reduced to three) for
the sets of initial conditions comprising the (3,3,3) excitation
and microcanonical normal mode sampling. Indeed, as shown
in Table 1, there is an almost coincidence between these two
sets of results.
Particularly interesting from Table 1 are the fractions of
vibrational, rotational, and translational energies in the product
O2 molecules. They are ∼37% for vibration, 4% for rotation,
and ∼59% for translation, these values being kept approximately
invariant with respect to the initial excitation. This suggests
that all vibrational modes are strongly coupled, which allows a
fast energy redistribution in the HO*2 complex and hence a
RRKM-type behavior for the decay rates of the unimolecular
reaction in eq 1. In fact, Figure 2 shows that the trajectory
results are well fitted by a simple inverse exponential form of
eq 9. This is in good agreement with recent classical and
quantum calculations for J ) 0.15 It is also seen from this figure
(panel a) that the results are nearly coincident for the one-mode
excitations (16,0,0), (0,13,0), and (0,0,5), although some scattering is present for the longest dissociation times. A similar
finding is observed from panel b for the (3,3,3) and microcanonical vibrational excitations. However, we note that the
unimolecular dissociation rate coefficients are higher in this case
than those corresponding to the three one-mode excitations as
could be seen by plotting the curves for kb ) 0.91 and 0.68
ps-1 on the same plot (see also Table 1). We are therefore led
to conclude that the coupling among “democratically” excited
vibrational modes is more efficient to give dissociative outcomes. Indeed, for the (16,0,0), (0,13,0), and (0,0,5) excitations
the decay rates decrease to about 0.7 ps-1. Although not very
significant, the small increase in kb for the (0,0,5) case may be
Figure 2. Logarithm of the decay rate for nonrotating HO*2 molecules
as a function of time. Panel a is for specific normal mode excitations:
], (16,0,0); 0, (0,13,0); 4, (0,0,5). Panel b compares the logarithms
of the decay rates for a microcanonical vibrational energy distribution
(O) and the (3,3,3) excitation (3), both corresponding to the initial
vibrational energy Ev ) 59.432 kcal mol-1. The lines represent the
least-squares fits of the points to eq 9; only one fit is shown since they
are indistinguishable within the scale of the figure for the different
sets of points.
an indication that the OH stretch (Figure 1c) is better coupled
to the reaction coordinate than the other modes, as already been
advanced elsewhere.14,17
We now address the influence of rotation in the HO*2
unimolecular dissociation, the results being gathered in Tables
2 and 3 for H + O2 formation and in Table 4 for dissociation
leading to O + OH products. Table 2 summarizes the results
obtained for total internal energy Etot ) 59.432 kcal mol-1,
which is only 4.569 kcal mol-1 above the classical threshold
for the H + O2 dissociative channel and significantly below
the O + OH one (∼68 kcal mol-1). It is seen from column
three of this table that the number of isomerizations increases
with increasing rotational energy. This is not unexpected since
rotation is more strongly coupled with the bending mode. Also,
the fraction of rotational energy in the H + O2 products increases
from 0.04 for the nonrotating HO*
2 to 0.47 for Er ) 33.961 kcal
mol-1, which suggests that the initial rotational energy appears
in the products preferentially as rotation. In contrast, f〈E′v〉
decreases with the increase of HO*2 rotational energy, which
suggests that most of the vibrational energy in the products
comes from the HO*2 vibrational degrees of freedom. Note also
that the fraction of the H + O2 translational energy decreases,
in a nearly proportional way, as the rotational (vibrational)
energy increases (decreases) in HO*2. In turn, it appears that
most of the product’s translational energy is provided directly
from the initial vibrational degrees of freedom.
Unimolecular Dissociation of HO2
J. Phys. Chem. A, Vol. 101, No. 28, 1997 5171
TABLE 2: Trajectory Results for Total Internal Energy Etot ) 59.432 kcal mol-1 a
initial conditions
Er/kcal mol
-1
6.816
16.980
33.961
H + O2 products
(xyz)
b
Nisom
f〈E′v〉
f〈E′r〉
f〈E′tr〉
(111)
(100)
(010)
(001)
(111)
(111)
2285(4)
1908(3)
3674(40)
986(30)
4657(9)
8115(26)
0.28
0.31
0.07
0.03
0.19
0.11
0.16
0.08
0.53
0.50
0.30
0.47
0.56
0.61
0.40
0.47
0.51
0.42
ka/ps-1
kb/ps-1
0.002c
0.0002e
0.057g
0.013i
0.51
0.64
0.073d
0.11f
0.23h
0.10j
a
Initial vibrational mode energies have been chosen using a microcanonical sampling procedure. b Total number of isomerizations for trajectories
forming H + O2. c f 0A ) 0.90. d f 0B ) 0.10. e f 0A ) 0.95. f f 0B ) 0.05. g f 0A ) 0.21. h f 0B ) 0.79. i f 0A ) 0.72. j f B0 ) 0.28.
TABLE 3: Trajectory Results for Formation of H + O2 Products at Total Internal Energy Etot ) 76.412 kcal mol-1
initial conditions
Er/kcal
mol-1
0.0
16.980
23.797
aTotal
H + O2 products
(xyz)
a
Nisom
Nr
f〈E′v〉
f〈E′r〉
f〈E′tr〉
(111)
(100)
(010)
(001)
(111)
540(1)
532(1)
505(1)
1086(3)
895(3)
480(<1)
369
497
496
359
290
495
0.34
0.27
0.28
0.12
0.11
0.24
0.04
0.11
0.06
0.51
0.47
0.14
0.62
0.62
0.66
0.37
0.42
0.62
ka/ps-1
0.30b
0.26d
kb/ps-1
5.47
4.04
4.34
1.34c
1.47e
3.51
number of isomerizations for trajectories forming H + O2. b f 0A ) 0.11. c f 0B ) 0.89. d f 0A ) 0.05. e f 0B ) 0.95.
TABLE 4: Trajectory Results for Formation of O + OH Products at Total Internal Energy Etot ) 76.412 kcal mol-1
initial conditions
Er/kcal
mol-1
0.0
16.980
23.797
O + OH products
(xyz)
a
Nisom
Nr
f〈E′v〉
f〈E′r〉
f〈E′tr〉
ka/ps-1
kb/ps-1
(111)
(100)
(010)
(001)
(111)
90(<1)
8(2)
12(3)
903(6)
1137(5)
8(1)
131
3
4
138
210
5
0.43
b
b
0.22
0.21
b
0.17
b
b
0.19
0.12
b
0.40
b
b
0.59
0.67
b
b
b
0.12c
0.06e
b
3.22
b
b
1.36d
1.10f
b
a
Total number of isomerizations for trajectories forming O + OH. b The number of trajectories forming O + OH is too low to obtain reliable
statistics. c f 0A ) 0.32. d f 0B ) 0.68. e f 0A ) 0.13. f f 0B ) 0.87.
Figure 3. Logarithm of the decay rate for rotating HO*2 molecules as
a function of time at Etot ) 59.432 kcal mol-1. Panel a: O, Er ) 6.816
kcal mol-1; 4, Er ) 16.980 kcal mol-1; 0, Er ) 33.961 kcal mol-1.
Panel b: O, Er ) 6.816 kcal mol-1 and (100) excitation. Panel c: 4,
Er ) 6.816 kcal mol-1 with rotational energy associated to Ly; O, Lz.
See text.
Figure 3a shows the logarithm of the decay rates as a function
of time for different values of the rotational excitation. It is
clear from this figure and Tables 1 and 2 that kb decreases (from
0.91 to 0.51 ps-1) as the rotational energy increases (from zero
to 6.816 kcal mol-1, respectively), while continuing to decrease
for even higher rotational energies. This is in accordance with
the resulting increase in the centrifugal barrier. Although some
decrease in the value of the dissociation rate coefficients should
arise, the system would be expected to follow the same
exponential behavior described by eq 9. This is the case shown
in Figures 2b and Figure 3a for the nonrotating and Er ) 6.816
kcal mol-1 cases, respectively. However, as the rotational
excitation increases for Er ) 16.980 kcal mol-1 and Er ) 33.961
kcal mol-1, the system does not present a single-exponential
behavior, and the two-step mechanism17 described in section 2
(see eqs 7 and 8) appears to correctly account for the main
features of the trajectory results. Accordingly, since the
noncoupled A-type HO*
2 molecules must be associated with
specific “inactive” rotational modes, the rate ka should be
inversely related to the amount of energy in those modes, which
may increase with initial Er. In fact, we conclude from Figure
3a and Table 2 that not only does ka decrease on passing from
Er ) 16.980 kcal mol-1 to Er ) 33.961 kcal mol-1 but also the
fractions of initially prepared A-type and B-type HO*
2 molecules
are interchanged, increasing from f 0A ) 0.21 for the former
value of the rotational energy to f 0A ) 0.72 for the latter.
In order to associate the noncoupled A-type species with a
specific kind of initial preparation of the HO*
2 molecules, we
have run trajectories for the lower rotational excitation (Er )
6.816 kcal mol-1), assigning the orientation of the rotational
angular momentum to three mutually perpendicular directions.
Thus, as described in section 2, for each case we have allowed
the molecule to rotate around only one of the principal axis of
inertia shown in Figure 1, which means that Lx ) Ly ) 0 and
Lz * 0 for the rotation in the plane of the nuclei and Ly ) Lz
) 0 with Lx * 0 or Lx ) Lz ) 0 with Ly * 0 for rotations out
of that plane. The results are summarized in Table 2 and the
decay rates shown in Figure 3 (panels b and c). Note that the
excitation (100) of the Lx component leads to fractions of energy
in the products similar to those found for the nonrotating system,
presenting for the unimolecular dissociation rate also a RRKMtype behavior as displayed in Figure 3b. Furthermore, the
corresponding value of kb is lower than in the nonrotating case,
but slightly higher than in the equally distributed rotational
energy [denoted by (111)]. This may be rationalized from the
5172 J. Phys. Chem. A, Vol. 101, No. 28, 1997
fact that the (100) rotational excitation is coupled with the
reaction path, although the arising centrifugal barrier causes the
decrease of kb from 0.91 ps-1 for the nonrotating case to 0.64
ps-1 for the rotating one. Because of this we also find a
distribution of energy in the products which only favors slightly
rotation in comparison with the nonrotating system.
Figure 3c shows the logarithms of decay rates for the (010)
and (001) rotational excitations. We can see now that the results
for both cases are well fitted by eq 8, which means that the
two-step mechanism may be used to describe the behavior of
the dissociating system. This arises because all rotational energy
is associated with the components Ly or Lz of the angular
momentum, which seem to be uncoupled to the reaction path.
Note that almost the whole set of prepared HO*2 molecules are
in both cases A-type, the corresponding fractions being 90%
and 95% for the (010) and (001) rotational excitations,
respectively. The remaining 10% or 5% B-type ones are
probably due to some coupling with the reaction path, which
occurs for points of phase space corresponding to specific
vibrational excitations compatible with the microcanonical
normal mode sampling. However, it is worth noting that the
decay rates kb are lower than the corresponding value for the
equally excited (111) situation, which suggests a weaker
coupling with the reaction path for such B-type HO*
2 molecules.
In fact, the (010) excitation seems to be essentially associated
with the bending vibrational motion, which leads to an increase
in the number of isomerizations. Moreover, the (010) and (001)
preparations give rise to high rotationally excited O2 product
molecules, while the corresponding values for f〈E′v〉 are the lowest
ones. Clearly, this suggests that the vibrational-rotational
interaction is practically inactive.
As far as the total internal energy increases to Etot ) 76.412
kcal mol-1 the reactive O + OH channel opens, leading to
competitive processes between this channel and the H + O2
one, which causes additional problems in the interpretation of
the results. The trajectory results for formation of H + O2 and
O + OH are presented in Tables 3 and 4, respectively. In
addition, we show in Figure 4 the corresponding logarithm of
the decay rates as a function of time for both dissociative
channels. For H + O2 formation, the fractions f〈E′v〉, f〈E′r〉, and
f〈E′tr〉, shown in Table 3 present a pattern similar to that found
for Etot ) 59.432 kcal mol-1 as the initial rotational energy
increases. Also seen from Table 3 is the fact that kb decreases
as the initial rotational excitation increases, the values always
being larger than for Etot ) 59.432 kcal mol-1 due to the
significant increase in the internal energy. It is possible to
observe in Figure 4a that the decay rates present an essentially
RRKM behavior even for the highest rotational excitation, which
can be explained by the increase in the total energy of the
system, clearly above the H + O2 reaction threshold. However,
the (100) excitation leads once again to an increase in the decay
rate for the dissociation HO*
2 f O2 + H, while the (010) and
(001) excitations present two distinct decay regimes in Figure
4b, although not so pronounced as shown before for Etot )
59.432 kcal mol-1.
In contrast, the number of events leading to the formation of
O + OH are significant only for the nonrotating system and
for Etot ) 16.980 kcal mol-1 with (010) and (001) initial
excitations. In the other cases, the number of trajectories
forming O + OH is too small to get conclusions. This means
that rotational degrees of freedom of equally excited molecules
(111), but mainly those associated with (100) excitation, tend
to be coupled with the reaction path to give H + O2 products,
as it has already been found for Etot ) 59.432 kcal mol-1. Since
for nonrotating molecules the “democratically” distributed
Marques and Varandas
Figure 4. Logarithm of the decay rate for rotating HO*2 molecules as
a function of time at Etot ) 76.412 kcal mol-1. Panels a and b are for
the H + O2 products, while panels c and d show the results for formation
of O + OH. Panel a: ], Er ) 0.0 kcal mol-1; O, Er ) 16.980 kcal
mol-1; 0, Er ) 23.797 kcal mol-1. Panel b: O, Er ) 16.980 kcal mol-1
with excitation associated to Lx; 4, Ly; 0, Lz. Panel c: ], Er ) 0.0
kcal mol-1. Panel d: O, Er ) 16.980 kcal mol-1 with excitation
associated to Ly; 0, Lz. See text.
vibrational energy is higher than the O + OH reactive threshold,
the HO*2 species may dissociate to form OH if the high excited
vibrational modes are coupled with the corresponding reaction
path, which appears to be the case for 131 trajectories.
However, since the “prompt to reaction” molecules are supposed
to originate H + O2 products, dissociation to O + OH occurs
after a delay of ∼0.12 ps, followed by a steady rate of 3.22
ps-1, represented by the straight line of Figure 4c. Conversely,
for Er ) 16.980 kcal mol-1 with (010) and (001) excitations
the vibrational energy is not sufficient to open the O + OH
channel and some portion of the initial rotational energy has to
be used to break the O-OH bonds. Although the initial
vibrational energy is quite above the H + O2 reactive threshold,
the number of trajectories leading to O + OH is significant,
which points to the fact that the rotational degrees of freedom
associated with the (010) and (001) excitations are preferentialy
coupled to the O + OH reaction path as might be anticipated
from Figure 1. In fact, although a clear two-step mechanism
is shown in Figure 4d for the initial (010) and (001) rotational
excitations, it is important to note that most HO*2 molecules are
prepared as B-type ones in both cases, such molecules being
promptly dissociated into O + OH products.
4. Concluding Remarks
We have shown that nonrotating HO*
2 dissociation presents
no mode specificity. In fact, even for energies near the H +
O2 threshold, the system shows a clear RRKM-type (i.e., single
inverse exponential) behavior. Moreover, a “democratic”
excitation of the three vibrational modes allows a better coupling
among them, and hence enhances the unimolecular dissociation
rate. The fractions of vibrational, rotational, and translational
energies in the products have also been found to be nearly
constant irrespective of the initial excitation.
As some rotational excitation is added to the molecule, the
decaying behavior is no longer RRKM, being now described
Unimolecular Dissociation of HO2
by a double inverse exponential function which indicates the
existence of bottlenecks in phase space. Such bottlenecks have
been shown to be associated with the rotational excitations (010)
and (001) (i.e., around the Ly and Lz axis, respectively). In fact,
these rotational degrees of freedom are associated with total
angular momentum (J) conservation and hence are inactive (i.e.,
do not readily transfer energy to promote dissociation), while
Lx is related to the projection of J onto the body-fixed axis and
is not a constant of the motion. Such findings are related to
those described in our previous work,17 where the preparation
of the HO*
2 complexes has been done randomly using H + ArO2
collisions. Indeed, we have then observed that for small
collision energies there is a small coupling between rotational
and vibrational degrees of freedom so that the complexes require
an induction time prior to dissociation.
We have also studied rotational effects for a total internal
energy above the threshold for O + OH dissociation. In this
case, there is a competition between the H + O2 and O + OH
reactive events, although the former is clearly favored. Indeed,
for most sets of initial conditions that include molecular rotation,
only a few trajectories led to OH formation. The exceptions to
this trend arise for the (010) and (001) rotational excitations
where a large number of dissociations occurs to form OH. This
kind of excitation, less coupled with the reaction path for O2
formation, favors O + OH dissociation, especially for trajectories leading to a large number of isomerizations.
In summary, rotational effects (including the initial J orientation) have shown to be important in characterizing the dissociation of HO*2, even for internal energies above the O + OH
threshold. Since quantum dynamical calculations on the HO2
system are currently affordable only for J ) 0, they cannot be
used to account for such rotational effects (see also ref 25).
Thus, trajectory calculations are the only available approach to
fully describe the phenomena associated with HO*2 dissociation.
Acknowledgment. The financial support from Junta Nacional de Investigação Cientı́fica e Tecnológica (JNICT), Portugal,
is gratefully acknowledged.
References and Notes
(1) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics
and Dynamics; Prentice Hall: Englewood Cliffs, NJ, 1989.
J. Phys. Chem. A, Vol. 101, No. 28, 1997 5173
(2) Morais, V. M. F.; Varandas, A. J. C. J. Phys. Chem. 1992, 96,
5704.
(3) Marcus, R. A. J. Chem. Phys. 1952, 20, 359.
(4) Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894.
(5) Guan, Y.; Lynch, G. C.; Thompson, D. L. J. Chem. Phys. 1987,
87, 6957.
(6) Preiskorn, A.; Thompson, D. L. J. Chem. Phys. 1989, 91, 2299.
(7) Guan, Y.; Thompson, D. L. Chem. Phys. 1989, 139, 147.
(8) Marks, A. J. J. Chem. Phys. 1994, 100, 8096.
(9) Miller, J. A.; Brown, N. J. J. Phys. Chem. 1982, 86, 772.
(10) Melius, C. F.; Blint, R. J. Chem. Phys. Lett. 1979, 64, 183.
(11) Pastrana, M. R.; Quintales, L. A. M.; Brandão, J.; Varandas, A. J.
C. J. Phys. Chem. 1990, 94, 8073.
(12) Mandelshtam, V. A.; Grozdanov, T. P.; Taylor, H. S. J. Chem.
Phys. 1995, 103, 10074.
(13) Mahapatra, S. J. Chem. Phys. 1996, 105, 344.
(14) Dobbyn, A. J.; Stumpf, M.; Keller, H.-M.; Hase, W. L.; Shinke,
R. J. Chem. Phys. 1995, 103, 9947.
(15) Dobbyn, A. J.; Stumpf, M.; Keller, H.-M.; Schinke, R. J. Chem.
Phys. 1996, 104, 8357.
(16) Song, K.; Peslherbe, G. H.; Hase, W. L. J. Chem. Phys. 1995, 103,
8891.
(17) Marques, J. M. C.; Wang, W.; Pais, A. A. C. C.; Varandas, A. J.
C. J. Phys. Chem. 1996, 100, 17513.
(18) Varandas, A. J. C.; Brandão, J.; Pastrana, M. R. J. Chem. Phys.
1992, 96, 5137.
(19) Varandas, A. J. C.; Marques, J. M. C. J. Chem. Phys. 1992, 97,
4050.
(20) Varandas, A. J. C. J. Chem. Phys. 1993, 99, 1076.
(21) Varandas, A. J. C. Chem. Phys. Lett. 1994, 225, 18.
(22) Varandas, A. J. C.; Marques, J. M. C. J. Chem. Phys. 1994, 100,
1908.
(23) Marques, J. M. C.; Wang, W.; Varandas, A. J. C. J. Chem. Soc.,
Faraday Trans. 1994, 90, 2189.
(24) Varandas, A. J. C. Chem. Phys. Lett. 1995, 235, 111.
(25) Varandas, A. J. C. Mol. Phys. 1995, 85, 1159.
(26) Varandas, A. J. C.; Pais, A. A. C. C.; Marques, J. M. C.; Wang,
W. Chem. Phys. Lett. 1996, 249, 264.
(27) Hase, W. L. MERCURY: a general Monte-Carlo classical trajectory
computer program, QCPE No. 453. An updated version of this program is
VENUS96: Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornick, A.; Lim,
K. F.; Lu, D.-H.; Peslherbe, G. H.; Swamy, K. N.; Van de Linde, S. R.;
Varandas, A. J. C.; Wang, H.; Wolf, R. J. QCPE Bull. 1996, 16, 43.
(28) Bintz, K. L.; Thompson, D. L. J. Chem. Phys. 1986, 85, 1848.
(29) Raff, L. M.; Thompson, D. L. Theory of Chemical Reaction
Dynamics, M. Baer, Ed.; Chemical Rubber Co.: Boca Raton; FL, 1985; p
1.
(30) Sloane, C. S.; Hase, W. L. J. Chem. Phys. 1977, 66, 1523.